Solving Infinite Games in the Baire Space
| Autor: | Brütsch, Benedikt, Thomas, Wolfgang |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Fundamenta Informaticae, Volume 186, Issues 1-4: Trakhtenbrot's centenary (October 21, 2022) fi:8743 |
| Druh dokumentu: | Working Paper |
| Popis: | Infinite games (in the form of Gale-Stewart games) are studied where a play is a sequence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space $\omega^\omega$. We consider such games defined by a natural kind of parity automata over the alphabet $\mathbb{N}$, called $\mathbb{N}$-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical B\"uchi-Landweber Theorem (for finite-state games in the Cantor space $2^\omega$) holds again for the present games: A game defined by a deterministic parity $\mathbb{N}$-MSO-automaton is determined, the winner can be computed, and an $\mathbb{N}$-MSO-transducer realizing a winning strategy for the winner can be constructed. Comment: Updated header on title page. 26 pages, 1 figure |
| Databáze: | arXiv |
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